## About Me

I am a second year PhD student in Mathematics and an NSF Graduate Research Fellow at the University of Pennsylvania. I am co-advised by Mona Merling and Kirsten Wickelgren. Previously I was an undergraduate at Johns Hopkins University. I am interested in algebraic topology, particularly $\textbf{A}^1$-homotopy theory.

My CV is here.

tbraz at math.upenn.edu

Fall 2019, Mona Merling and I will be organizing the inaugural Directed Reading Program at Penn. In 2018, I wrote some expository notes on Constructing The Unstable Motivic Homotopy Category Using $(\infty,1)$-Categories, supervised by Emily Riehl and Kirsten Wickelgren. In fall 2018, I ran a seminar on homotopy theory and algebraic $K$-theory with Qinyung Zeng and Perry Hart.### Papers and Preprints:

- The Trace of the Local $\textbf{A}^1$-Degree, with R. Burklund, S. McKean, M. Montoro, M. Opie, Submitted. arXiv:1912.04788.
- An Introduction to $\textbf{A}^1$-Enumerative Geometry, with K. Wickelgren, in progress, to appear in
*Proceedings of the London Mathematical School*. - Zeros of Newform Eisenstein Series on $\Gamma_0(N)$, with V. Jakicic,
*J. Number Theory*(190), 2018. - On Consecutive $n$th Roots of Unity Modulo $q$, with J. Harrington, S. Kannan, M. Litman,
*J. Number Theory*(174), 2017.

### Expository writing:

- Constructing the Unstable Motivic Homotopy Category using $(\infty,1)$-Categories, arXiv:1810.00094.
- The Generalized Poincaré Conjecture Using $s$-Cobordism, for the Penn Grad Student Seminar, Fall 2018.

### Conference and course notes:

*Disclaimer:*Any errors found in these notes should be attributed to me, not the original lecturer. If you find any typos or have suggestions, please feel free to contact me.

- School on Motives and Stacks, September 2019, minicourses by Hoskins, Østvæer, Rydh. Notes available upon request.
- European Autumn School in Topology, September 2019, minicourses by Barthel, Salvatore. Notes available upon request.
- PIMS Workshop on Arithmetic Topology, June 2019, minicourses by Ellenberg, Farb, Galatius, Ho, Vakil/Landesman, Wickelgren.
- An Introduction to $\textbf{A}^1$-homotopy theory from an infinity-categorical viewpoint, June 2018, (notes from lectures of Strunkland and Tamme, Homotopy Theory Summer Berlin 2018).